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Identical expressions
y=(three x^3+ one)^ two
y equally (3x cubed plus 1) squared
y equally (three x cubed plus one) to the power of two
y=(3x3+1)2
y=3x3+12
y=(3x³+1)²
y=(3x to the power of 3+1) to the power of 2
y=3x^3+1^2
Similar expressions
y=(3x^3-1)^2

The derivative of the function/ y=(3x^3+1)^2

Derivative of y=(3x^3+1)^2

The solution

You have entered [src]

          2
/   3    \ 
\3*x  + 1/

$$\left(3 x^{3} + 1\right)^{2}$$

  /          2\
d |/   3    \ |
--\\3*x  + 1/ /
dx

$$\frac{d}{d x} \left(3 x^{3} + 1\right)^{2}$$

Transform

Detail solution

Let $u = 3 x^{3} + 1$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x^{3} + 1\right)$ :
1. Differentiate $3 x^{3} + 1$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $9 x^{2}$
  2. The derivative of the constant $1$ is zero.
  The result is: $9 x^{2}$
The result of the chain rule is:

$9 x^{2} \cdot \left(6 x^{3} + 2\right)$
Now simplify:

$x^{2} \cdot \left(54 x^{3} + 18\right)$

The answer is:

$x^{2} \cdot \left(54 x^{3} + 18\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2 /   3    \
18*x *\3*x  + 1/

$$18 x^{2} \cdot \left(3 x^{3} + 1\right)$$

Simplify

The second derivative [src]

     /        3\
18*x*\2 + 15*x /

$$18 x \left(15 x^{3} + 2\right)$$

Simplify

The third derivative [src]

   /        3\
36*\1 + 30*x /

$$36 \cdot \left(30 x^{3} + 1\right)$$

Simplify

The graph

Derivative of y=(3x^3+1)^2